1171edo
The 1171 equal divisions of the octave (1171edo) divides the octave into 1171 parts of size 1.0248 cents each. It is a very strong 5-limit division, being the first one past 612 with a lower 5-limit relative error. It has a 5-limit comma basis consisting of the monzisma, [54 -37 2⟩ and whoosh, [37 25 -33⟩. While not a strong higher-limit system, it is uniquely consistent through the 27-odd-limit, and is very strong on the 2.3.5.11 subgroup. We might also note that 1171 is a prime number.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.009 | +0.023 | -0.423 | +0.006 | -0.220 | -0.429 | -0.331 | -0.093 | +0.312 | -0.373 |
| Relative (%) | +0.0 | +0.9 | +2.2 | -41.3 | +0.6 | -21.5 | -41.9 | -32.3 | -9.1 | +30.4 | -36.4 | |
| Steps (reduced) |
1171 (0) |
1856 (685) |
2719 (377) |
3287 (945) |
4051 (538) |
4333 (820) |
4786 (102) |
4974 (290) |
5297 (613) |
5689 (1005) |
5801 (1117) | |